7/25/2023 0 Comments Gold element brittleFirst, some technical editing will be applied to the list of elements in Table 1. Now it will be shown that there is some correlation between the physical ductility’s and the number of shells in each electronic configuration. ![]() For the general ductility treatment of Section VII the ductility measure for cast iron is about that of T/C = 2/5 = 0.4, giving general agreement between the two very different methodologies, but which still have the same limits. Take iron for example, with its physical ductility of D = 0.43. Still, most of those elements in Table 1 are in general agreement with perceived ductility levels. It must be cautioned that these physical ductility’s for the elements could be considerably different from those for the compounds and alloys of the same generic names. The final step is to take the table of elements from Section XII to obtain the following table of physical ductility’s for the solids forming elements.Ī graph of the physical ductility’s from (6) along with the values for a few of the elements from Table 1 are given in Fig. This might at first seem surprising but actually it is consistent with the modeling of atomic potentials that are generally found to be of high order polynomial form. When (5) and (6) are combined it is found that the physical ductility, D, is a sixth degree polynomial in κ. Then the physical ductility, D, is determined by Of necessity there is an inflection point involved with (4) that will later relate to the ductile/brittle transition.Ĭollecting the governing forms for the physical ductility together, then the nanoscale variable κ is found from experimental values of ν for the elements from (1). There is no unique form for this, but the lowest order polynomial to satisfy the end conditions is given by Thinking of this relationship as y = f(x), then an explicit form for it must be found. This is to use the absolute limits on ν of 0 and 1/2, as derived in Section XII, to require that a relationship between the ductility index (2) and the physical ductility, say D, must have vanishing slopes on a D versus ductility index curve at the limits of the latter, which are 0 and 1. The next step leading to the measure of physical ductility is developed here. Knowledge of the values of Poisson’s ratios for the (polycrystalline) elements then gave the corresponding ductility indices for the elements, establishing the rank order list of the ductility’s. The relationship between the nanoscale variable κ and the macroscopic Poisson’s ratio ν was found to be given by Involving the ratio of bond bending to bond stretching stiffness was used to form the ductility index as Then this nanoscale analysis was extended to the three dimensional conditions in Section XII and applied to the problem of assessing the ductility of the elements. This planar form of elemental carbon was amenable to a complete analysis which revealed the relationship of the two dimensional Poisson’s ratio of graphene to a nanoscale variable determined by the ratio of the bond bending resistance to the bond stretching resistance for the carbon atom. The related work preceding that of Section XII was the study of the properties of graphene in Section XI. ![]() The program now is taken a step further by deriving an explicit physical ductility measure from the ductility index of Section XII. This rank order list was expressed in terms of a ductility index. The end result was a rank order list of ductility’s for those elements forming the more commonly used solids/materials. In Section XII the ductility of the elements was initiated as an area of study.
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